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Radicals

Radicals. Table of contents. Slide 3: What are Radicals? Slides 4-8: Simplifying Radicals Slides 9-11: Multiplying Radicals Slides 12-15: Dividing Radicals Slides 16-19: Adding Radicals Slides 20-23: Subtracting Radicals Slides 24-29: Solving Radicals Slide 30: Sources Slide 31: THE END.

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Radicals

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  1. Radicals

  2. Table of contents • Slide 3: What are Radicals? • Slides 4-8: Simplifying Radicals • Slides 9-11: Multiplying Radicals • Slides 12-15: Dividing Radicals • Slides 16-19: Adding Radicals • Slides 20-23: Subtracting Radicals • Slides 24-29: Solving Radicals • Slide 30: Sources • Slide 31: THE END

  3. What are radicals? Radical index Radicand

  4. Simplifying Radicals? • Index: the index is the part of the equation that tells yow how many kind you are looking for Example: • Since there are two 3s the 3s can come out of the radicand but you only write it once. 3x3=9 3 3 = 3 3 3 3

  5. Example: 4 2 16 2 8 2 4 2 2

  6. Example: 6 2 36 2 18 2 9 3 3

  7. Practice: Answer worked out and explained on next slide

  8. Answers

  9. Multiplying radicals: • When multiplying radicals you have to check if the indeces and radicands of both radicals match. • Use the product rule. Ex. Different indeces

  10. Practice: Answer worked out and explained on next slide

  11. Answer

  12. Dividing Radicals: • When dividing radicals you have to check if the indeces of both radicals match. • Then, use the quotient rule: Ex.

  13. Dividing Radicals: • NOTE: • Multiply the numerator and denominator by the denominator. This causes the radicals on the bottom to cancel out to just a WHOLE number. Only do this if necessary. If there isn’t a radical in the denominator, disregard this.

  14. PRACTICE: Answer worked out and explained on next slide

  15. Answers

  16. Adding radicals: • Steps: 1. Simplify ALL radicals 2. Combine "like terms“. Like terms = same index and same radicand. **If you don't have like terms, just leave it alone! No one wants to be forced together!**

  17. Example: 2 8 2 4 2 2

  18. Practice: Answer worked out and explained on next slide

  19. Answers

  20. Subtracting Radicals: • Steps: 1. Simplify ALL radicals 2. Combine "like terms“. Like terms = same index and same radicand. **If you don't have like terms, just leave it alone! No one wants to be forced together!**

  21. Examples:

  22. Practice: Answer worked out and explained on next slide

  23. Answers:

  24. Solving Radicals (on one side) STEPS: • Isolate the radical • Raise everything on both sides of the equal sign to the power of the index(see page 3 if you already forget what this is) • Solve for x • Ex.

  25. Solving Radicals (On both sides) • Raise everything on both sides of the equal sign to the power of the index(see page 3 if you already forget what this is) • Solve for x • Does this look familiar? It’s just like solving equations with radicals on one side except you don’t need to isolate the variable. Ex.

  26. Practice Answer worked out and explained on next slide

  27. Answer

  28. Practice Answer worked out and explained on next slide

  29. Answer

  30. Sources: • Thanks to Mrs. Ashwell’s notes that we took & notes on score • Problems- worksheets & PowerPoint from Mrs. Ashwell’s class.

  31. The end Remember to keep practicing & to study !!

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